Bayesian and Dempster-Shafer models for combining multiple sources of evidence in a fraud detection system
By Fabrice Daniel, Artificial Intelligence Department of Lusis, Paris, France
Combining evidence from different sources can be achieved with Bayesian or Dempster-Shafer methods. The ﬁrst re-quires an estimate of the priors and likelihoods while the second only needs an estimate of the posterior probabilities and enables reasoning with uncertain information due to imprecision of the sources and with the degree of conﬂict between them. This paper describes the two methods and how they can be applied to the estimation of a global score in the context of fraud detection.
Fraud detection mainly relies on expert driven methods that implement a set of rules and data driven approaches implementing machine learning (ML) models. Both provide an estimate (or a score) for a new transaction to be fraudulent.
While each ML model naturally returns a fraud probability, the experts can also attach a probability to each rule. They can also be automatically calculated from the labeled his-tory. Combining them together produces a global score that can be used in a near real time system to rank a set of trans-actions having the highest probability to be fraudulent. By obtaining this ranking, investigators can concentrate their efforts on the suspect transactions with the highest probability of being true frauds.
The most common approaches for combining scores are summing individual scores or returning the highest score among the trigged rules. This is not entirely satisfactory given that summing scores is equivalent to averaging the probabilities returned by each predictor (rule or model). It also does not take into account the uncertainty of each predictor and the degree of conﬂict between them.
For the Lusis fraud system, we work on implementing more appropriate approaches.
This paper proposes two ways for addressing this problem. The ﬁrst is to use Bayesian methods ; the second is to combine the scores by using Dempster-Shafer theory .
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